I like how you guys put words into my mouth. I´m not ignorant of stats, I´m over them.
No statistician claims that any combination of stats can account for 100% of variation in performance.
So, the placeholders don´t represent constant values. 1 isn´t actually 1, at least not always. You understand that this little sign (=) becomes a lie, right? All laws derivating from math involving them aren´t really laws, they´re more like general rules of thumb, yes?
When they can claim though is that stats can help us find value that is often missed when using our clearly flawed and biased perceptions. They help us make the best choice amidst the always present uncertainty.
You´re making stuff up now, aren´t you? Which "clearly flawed perception" are you talking about? Stats are just a bunch of numbers without proper interpretation, just like the action on the court has to be interpreted. Considering how I read deeply flawed application of stats on this board alone on a daily basis, I have a hard time accepting their, at best, "general rule of thumb" as the incorruptible judge in any debate.
So, first of all, I question the neutrality of numbers interpreted by humans, and thus, all laws derivating from them. But you understand that, basically, as you wrote
So the fallacy is not in the stat. It is in the idea that stats are all or nothing. Understanding the implications of stats help you make better decisions because our intuitions are incredibly subjective and often far from reality. This is obvious is we read this forum or watch sports tv and see intelligent fans arguing for opposite positions.
I challenge this view, too. The fallacy is also in the stat alone. The matter you´re trying to explain with not 100% exact placeholders in a closed system is a dynamic one in an open system, in other words, their applicability is limited per se.
Only if the framing conditions stay exactly the same (which they never do), and the stat is trying to explain a simple cause and effect (which every 10 year old could do with words), and 1 is actually always 1, then they tell you something definitive about a limited aspect of the game, which then has to be interpreted and put in it´s proper context by humans with their, as you called it, "clearly flawed perception".
An assist isn´t simply an assist, there are a myriad of angles on the court from which the ball could go from point A to B, and the distance between the assists man, the receiver and the opponent(s) is never the same, but paramount to contextualize the assist. Just this one, lousy assist. To cover this aspect alone, you´d need 3D graphics instead of simple numbers.
Theoretically feasible, pratically useless.
Considering that every NBA team employs professional statisticians, and there are still countless braindead decisions made in the NBA every year, I´d say the advantage of relying on stats over common sense still has to be proven.
We don't consider "the eye test" or "common sense" or whatever people call the alternatives to stats useless if they can't explain 100% of what happens in a game, so why are only stats held to that standard?
Because if they´re not even saying what they are supposed to say, then they´re simply misleading, and have the same meaningfulness as your daily horoscope. These NBA teams might just as well employ a bunch of priests and rabbis to give them advice.
Consequently, and maybe even more importantly, considering their arbitrary nature, their only purpose is to justify whatever anyone wants to justify, and are only distracting from the actual debate, often to the point that it´s impossible to carry on with the discussion without addressing them first in long, drawn-out and boring math exercises.
So, to make an already long post shorter:
I issue my challenge again. Show me a stat, tell me what it is supposed to say, and I will explain it´s fallacy.